Quantum Mechanics
... where χn (x) solve (21) with E = En and an are complex constants. In general this is not a stationary state and thus does not have definite energy. Instead the probability of measuring the particles energy as E = En is proportional to |an |2 (See Section 3). ...
... where χn (x) solve (21) with E = En and an are complex constants. In general this is not a stationary state and thus does not have definite energy. Instead the probability of measuring the particles energy as E = En is proportional to |an |2 (See Section 3). ...
Particle-wave duality - Proceedings of the Royal Society A
... see the wave-like character of an electron, we need a beam of electrons rather than a single one. This implies the wave-like character that we infer from interference has a similar statistical meaning. Likewise, in the following we measure symmetry in terms of its capacity to carry information, and ...
... see the wave-like character of an electron, we need a beam of electrons rather than a single one. This implies the wave-like character that we infer from interference has a similar statistical meaning. Likewise, in the following we measure symmetry in terms of its capacity to carry information, and ...
Spatial ordering of charge and spin in quasi-one
... state.26 This is a consequence26 of the Lieb-Mattis theorem27 which implies that without spin-dependent interactions the ground state of one-dimensional electron systems corresponds to the lowest possible spin quantum number (S = 0 or 1 / 2). This feature generally does not have to result in any spa ...
... state.26 This is a consequence26 of the Lieb-Mattis theorem27 which implies that without spin-dependent interactions the ground state of one-dimensional electron systems corresponds to the lowest possible spin quantum number (S = 0 or 1 / 2). This feature generally does not have to result in any spa ...
A parallel repetition theorem for entangled projection
... Remarkably, the precise definition of the value depends on the physical interpretation that is given to the condition of spatial isolation. Under classical theory, isolated players are fully described by the functions that each apply to their respective question in order to determine their answer, a ...
... Remarkably, the precise definition of the value depends on the physical interpretation that is given to the condition of spatial isolation. Under classical theory, isolated players are fully described by the functions that each apply to their respective question in order to determine their answer, a ...
Geometry and Dynamics of a Quantum Search
... ordered tuple of multi-qubits from geometric and dynamical viewpoints, which has been left since [19]. In particular, the reduced search sequence in the QIS is intensively studied from the viewpoint of quantum information geometry. As an extension of [15] on the original search sequence, the Grover- ...
... ordered tuple of multi-qubits from geometric and dynamical viewpoints, which has been left since [19]. In particular, the reduced search sequence in the QIS is intensively studied from the viewpoint of quantum information geometry. As an extension of [15] on the original search sequence, the Grover- ...
Infinite-randomness quantum critical points induced by dissipation
... We emphasize that the multiplicative form of Eq. 共22兲 is not independent of the functional form of the action 共3兲. In contrast to the recursion relation 共14兲 for the interactions, the recursion relation 共22兲 for the gaps is special to the case of Ohmic dissipation. It is related to the fact that the ...
... We emphasize that the multiplicative form of Eq. 共22兲 is not independent of the functional form of the action 共3兲. In contrast to the recursion relation 共14兲 for the interactions, the recursion relation 共22兲 for the gaps is special to the case of Ohmic dissipation. It is related to the fact that the ...
Quantum Information Processing - LANL Research Library
... is, |α |2 + |β |2 = 1. Such a superposition or vector is said to be normalized. (For a complex number given by γ = x + iy, one can evaluate |γ |2 = x2 + y2. Here, x and y are the real and imaginary part of γ , and the symbol i is a square root of –1, that is, i2 = –1. The conjugate of γ is γ = x – i ...
... is, |α |2 + |β |2 = 1. Such a superposition or vector is said to be normalized. (For a complex number given by γ = x + iy, one can evaluate |γ |2 = x2 + y2. Here, x and y are the real and imaginary part of γ , and the symbol i is a square root of –1, that is, i2 = –1. The conjugate of γ is γ = x – i ...
The Path Integral approach to Quantum Mechanics Lecture Notes
... One of the important experiments that show the fundamental difference between Quantum and Classical Mechanics is the double slit experiment. It is interesting with respect to the path integral formalism because it leads to a conceptual motivation for introducing it. Consider a source S of approximat ...
... One of the important experiments that show the fundamental difference between Quantum and Classical Mechanics is the double slit experiment. It is interesting with respect to the path integral formalism because it leads to a conceptual motivation for introducing it. Consider a source S of approximat ...
Resonances, dissipation and decoherence in exotic and artificial atoms
... be approached exactly in the same way. This raises the question how the electron confinement in the dot should be modelled. The most common choice is a two-dimensional (or, in case of spherical quantum dots, three-dimensional) harmonic oscillator potential, since the solutions for the one-particle p ...
... be approached exactly in the same way. This raises the question how the electron confinement in the dot should be modelled. The most common choice is a two-dimensional (or, in case of spherical quantum dots, three-dimensional) harmonic oscillator potential, since the solutions for the one-particle p ...
Aalborg Universitet
... projected onto the subspace orthogonal to the eigenvalue under consideration. For most cases of physical interest this turns out to be the case, as long as the unperturbed eigenvalue lies in the continuum, far away from the threshold energies. The problem with the exponential decay law appears for b ...
... projected onto the subspace orthogonal to the eigenvalue under consideration. For most cases of physical interest this turns out to be the case, as long as the unperturbed eigenvalue lies in the continuum, far away from the threshold energies. The problem with the exponential decay law appears for b ...
Lévy flights in binary optimization
... various mutation parameters. Every parameter setting was investigated via 100 independent runs with maximum number of evaluations per run set to 100000. According to tradition, we evaluate ene as mean number evaluations in the case of successful optimization, rel as reliability of optimum searching ...
... various mutation parameters. Every parameter setting was investigated via 100 independent runs with maximum number of evaluations per run set to 100000. According to tradition, we evaluate ene as mean number evaluations in the case of successful optimization, rel as reliability of optimum searching ...
FEYNMANWS PATH INTEGRAL APPROACH TO QUANTUM FIELD
... super…cial charm in the fact that its square gives you the probability that a particle will go from here to there (possibly via an in…nite number of intermediate points), but that’s about it. After all, we are far more interested in particles that interact with …elds or other particles, anything but ...
... super…cial charm in the fact that its square gives you the probability that a particle will go from here to there (possibly via an in…nite number of intermediate points), but that’s about it. After all, we are far more interested in particles that interact with …elds or other particles, anything but ...
research statement - University of Illinois at Chicago
... (1) show that each solution γN (t) admits at least one limit point γ∞ (t) as N → ∞; (2) prove that any limit point satisfies the GP hierarchy (which is an infinite hierarchy of coupled linear non-homogeneous PDE that admits the so-called factorized solutions where each factor satisfies the cubic NLS ...
... (1) show that each solution γN (t) admits at least one limit point γ∞ (t) as N → ∞; (2) prove that any limit point satisfies the GP hierarchy (which is an infinite hierarchy of coupled linear non-homogeneous PDE that admits the so-called factorized solutions where each factor satisfies the cubic NLS ...
Quantum telecommunication with atomic ensembles
... the DLCZ protocol in which a write laser field with + polarization scatters a + signal photon, thereby causing an atom to make a transition from the initially prepared g , m = 0 hyperfine substate to the g⬘ , m = 2 state of the other hyperfine ground level via level e, as shown in Figs. 1 and 5. T ...
... the DLCZ protocol in which a write laser field with + polarization scatters a + signal photon, thereby causing an atom to make a transition from the initially prepared g , m = 0 hyperfine substate to the g⬘ , m = 2 state of the other hyperfine ground level via level e, as shown in Figs. 1 and 5. T ...
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or probability density.Probability amplitudes provide a relationship between the wave function (or, more generally, of a quantum state vector) of a system and the results of observations of that system, a link first proposed by Max Born. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding (see #References), and the probability thus calculated is sometimes called the ""Born probability"". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today.